M. Jovanović

Introduction to Numerical Modelling
of Two-Dimensional Free Surface Flows


(in Serbian)

Faculty of Civil Engineering

Belgrade, 1998.

ISBN 86-80049-83-2

Pages: 395

From Foreword:

This book emerges from author's lecture notes in Fluvial Hydraulics course for postgraduate students at the Faculty of Civil Engineering in Belgrade. However, the author hopes that this book shall be useful to practicing hydraulic engineers. For this reason, mathematical derivations are reduced as much as possible, thus an "intuitive", rather than a rigorous mathemathical approach is applied ...
A special consideration is given to splitting-operator finite-difference methods, and the shock-capturing techniques. Confronted with a challenging task to provide an overview of various numerical methods in a single volume, the author has chosen to pre- sent only "classical" approaches, which can help an engineer-user to become aware of limitations of the open-channel flow numerical modelling, and to gain a critical knowledge of what can be expected from comercial software packages. In addition to this, the particular choice of numerical schemes made in this book, reflects the author's desire to present some computational results of his own, obtained in the course of his academic and pro- fessional career.

M. Jovanović

Introduction to Numerical Modelling
of Two-Dimensional Free Surface Flows


Contents:

Foreword

1. Equations of Two-Dimensional Free Surface Flows
- Navier-Stokes equations
- Reynolds equations
- Depth-averaged equations
- Closure problem
- Modelling of dispersion terms

2. Shear stress modelling
- Shear stress distribution in boundary layer
- Velocity distribution in boundary layer
- Empirical frictional resistance formulas
- Bottom and free surface shear stresses

3. Turbulence modelling
- Turbulent viscosity and diffusion
- Zero equation turbulence modelling
- One-equation model ("k-model")
- Two-equations model ("k-epsilon")
- K-epsilon model for free-surface flows
- Large eddy simulation (LES)

4. Method of Characteristics
- Long waves in shallow water
- Flow equations
- Solution for flow in one space dimension
- Solution for flow in two space dimensions

5. The Finite Difference Method
- Finite-difference approximations
- Consistency, stability, convergence
- Finite-difference meshes
- Principles of numerical solution
- Solution of equations of 2D free-surface flows
- The fractional step method
- Modelling of discontinous flows (weak solutions)

6. The Finite Element Method
- General considerations
- Approximate solutions
- Types of finite elements
- Consistency and continuity
- Local coordinate systems
- Conventional Lagrange polynomial elements
- Hermite polynomial elements
- Special elements
- Integral formulations of FEM
- Matrix formulation of FEM
- Integral equation for the reference element
- One example
- Numerical integration
- Algorithmic structure of FEM
- Assembling of the global matrix
- Introduction of the boundary conditions
- Numerical solution of non-linear problems
- Application of FEM to 2D free-surface flow problems

7. The Boundary Element Method
- Theoretical background
- Solution of integral equations
- Application of BEM to 2D free-surface flow problems
- Examples

Appendix A: Classification of partial differential equations
Appendix B: The Von Neumann stability analysis

Subject and author index